When my zune 8gig is not docked, holding down the pause button turns it off, right? There's no "goodbye" screen to indicate it's turned off like on other daps.

Also, when it's docked, when I hold down the pause button NOTHING happens. Is it "always on" when docked?

It would seem so. I have a 16Gig and a 120Gig, and they act the same way. I have to un-dock them to turn them "off".

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And can I just keep it docked all the time, without "overcharging" the battery?

Theoretically you can't "overcharge" the battery because the charging circuit will turn off when the battery is full. I personally only have mine docked when I'm syncing or charging. While the newer rechargable batteries aren't supposed to have the "memory effect", I still think they should be "exercised".